Comparison between launching a real satellite and using the space elevator

737 v 131 metric tons

An Ariane 5G rocket was used to launch the Envisat environmental satellite on 1 March 2002.  The 8,111 kg satellite was placed in a 800 km sun synchronous polar orbit.  The normal weight of an Ariane 5 rocket is 737 tonnes.

http://en.winkipedia.ord/winki/Ariane_5

The imaginary second stage uses three 726 kN engines and has a weight of nearly 131 metric tons.
Total weight ratio 737:131 = 5.63:1


____________________ Testing effect of launching a satellite from the Space Elevator

Envisat satellite into Sun Synchronous (polar) Orbit

Satellite is to be thrown at a height of 855.700 km whilst raising at a speed of  0 km/h or 0 km/s.
Moving climber to  855.7 km takes  0 days  4 Hours and  16 minutes at 200 km/h

Aiming satellite at a final height of  800 km and an inclination of  90 degrees.
Therefor orbital velocity needs to be 7.452 km/s
The Pay Load weighs 8,111.0 kg, fuel 118,230.0 kg and the structure  4113 kg.
Total mass at launch is 130,454.0 kg.
Thrust of rocket 2178 kN and fuel burn rate 656.59 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.527 km/s.

Command types
F = Freefall for 'Value' seconds
I = Change Inclination by 'Value' degrees.  Negative to go south
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
T = Thrust for 'Value' seconds or until the fuel runs out


Time (s) 0            Velocity 0.527 km/s  Inclination  0 degrees  Up velocity  km/s  Height 855.700 km

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 0.527 km/s  Inclination  0 Degrees  Up velocity -0.030 km/s  Height 855.639 km.
;;;                   Orbital velocity for current height is 7.423 km/s  Fuel 118230.0 kg.

__________ P 8.889        Select vertical flight angle
Time (s) 5            Velocity 0.527 km/s  Inclination  0 Degrees  Up velocity -0.038 km/s  Height 855.605 km.
;;;                   Orbital velocity for current height is 7.423 km/s  Fuel 118230.0 kg.

__________ I 90           Fly to the new orbit of 90 degree (Polar) inclination
Time (s) 46           Velocity 0.527 km/s  Inclination  90 Degrees  Up velocity -0.231 km/s  Height 850.008 km.
;;;                   Orbital velocity for current height is 7.426 km/s  Fuel 91309.8 kg.

__________ T 140          Use Thruster to gain required orbital speed
Time (s) 186          Velocity 7.453 km/s  Inclination  90 Degrees  Up velocity -0.000 km/s  Height 800.696 km.
;;;                   Orbital velocity for current height is 7.452 km/s  Fuel  kg.

__________ F 5            Verify that satellite is still in orbit 5 seconds later
Time (s) 191          Velocity 7.453 km/s  Inclination  90 Degrees  Up velocity 0.000 km/s  Height 800.696 km.
;;;                   Orbital velocity for current height is 7.452 km/s  Fuel  kg.

Fuel left  0 kg.

*END

10,000 km was an arbitrarily chosen round number approximately one third of GEO.  If any one knows of a point below GEO at which things dropped from the SE go into orbit, rather than fall to the ground, I am interested.

In the long drop example the satellite was sub-orbital until had been forced into orbit.  The decent was controlled by increasing the forward velocity but keeping it a little under the new orbital velocity.  When the vertical speed got too high the satellite's speed of decent slowed down, if continued the satellite flow off into space.  When the horizontal speed was too low it crashed.  The numbers form a set, if you change one all the following ones need adjusting.

After the initial gain of orbit an ion engine that can be started and stopped would probably be a better motor than the chemical one simulated.  Burns lasting a half or a quarter second would have permitted a smoother landing.  One thousandth the thrust simply means that the burns would have to last a thousand times longer – not difficult when most burns are separated by over 1,000 seconds.

Modern satellites frequently have a ion engine for station keeping, the same motor and solar panels may be able to perform both decent control and station keeping.

I had looked upon transfer orbits as a method of going to the moon, not as elegant space gymnastics to get a sub-orbital satellite into orbit.

Yes I used the circular orbit equations.

I have managed to find a High drop for example 1 that works, it even saved a tiny amount of fuel.  Unfortunately the satellite has to be driven all the way.

Method
Raise the climber to 10,000 km.
Using a powerful rocket to quickly go to the required inclination.
Quickly accelerate to the orbital speed for 10,000 km.

Now things get interesting, use momentum to cause the satellite to drop.
As the satellite approaches the Earth repeatedly increase its orbital velocity as the orbital speed increases.
This requires short burns and a (second) rocket motor able to perform such burns.
As the orbital speed is following the 1/(radius) curve the size and time between burns changes.



____________________ Testing effect of launching a satellite from the Space Elevator

Dropping a 300 kg Pay Load to 350 km from 10,000 km

Satellite is to be thrown at a height of 10,000.000 km whilst raising at a speed of 147.000 km/h or 0.041 km/s.
Moving climber to  10000 km takes  2 days  2 Hours and  0 minutes at 200 km/h

Aiming satellite at a final height of  350 km and an inclination of  1 degrees.
Therefor orbital velocity needs to be 7.697 km/s
The Pay Load weighs 300.0 kg, fuel 5,354.0 kg and the structure  420 kg.
Total mass at launch is 6,074.0 kg.
Thrust of rocket 196 kN and fuel burn rate 56.6 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 1.194 km/s.

Command types
F = Freefall for 'Value' seconds
I = Change Inclination by 'Value' degrees.  Negative to go south
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
T = Thrust for 'Value' seconds or until the fuel runs out


Time (s) 0            Velocity 1.194 km/s  Inclination  0 degrees  Up velocity 0.041 km/s  Height 10,000.000 km

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 1.194 km/s  Inclination  0 Degrees  Up velocity 0.035 km/s  Height 10,000.152 km.
;;;                   Orbital velocity for current height is 4.933 km/s  Fuel 5354.0 kg.

__________ I 1            Fly to the new orbit of 1 degree inclination
Time (s) 5            Velocity 1.194 km/s  Inclination  1 Degrees  Up velocity 0.034 km/s  Height 10,000.187 km.
;;;                   Orbital velocity for current height is 4.933 km/s  Fuel 5297.4 kg.

__________ T 70           Use Thruster to gain required orbital speed
Time (s) 75           Velocity 4.883 km/s  Inclination  1 Degrees  Up velocity -0.035 km/s  Height 9,999.661 km.
;;;                   Orbital velocity for current height is 4.933 km/s  Fuel 1335.4 kg.

__________ F 6000         Allow time to drop
Time (s) 6075         Velocity 4.883 km/s  Inclination  1 Degrees  Up velocity -0.428 km/s  Height 8,925.021 km.
;;;                   Orbital velocity for current height is 5.104 km/s  Fuel 1335.4 kg.

__________ T 3            Increase orbital velocity - A
Time (s) 6078         Velocity 5.177 km/s  Inclination  1 Degrees  Up velocity -0.428 km/s  Height 8,923.738 km.
;;;                   Orbital velocity for current height is 5.104 km/s  Fuel 1165.6 kg.

__________ F 3000         Allow time to drop
Time (s) 9078         Velocity 5.177 km/s  Inclination  1 Degrees  Up velocity -0.506 km/s  Height 7,643.014 km.
;;;                   Orbital velocity for current height is 5.332 km/s  Fuel 1165.6 kg.

__________ T 3            Increase orbital velocity - B
Time (s) 9081         Velocity 5.499 km/s  Inclination  1 Degrees  Up velocity -0.506 km/s  Height 7,641.495 km.
;;;                   Orbital velocity for current height is 5.332 km/s  Fuel 995.8 kg.

__________ F 5000         Allow time to drop
Time (s) 14081        Velocity 5.499 km/s  Inclination  1 Degrees  Up velocity -0.780 km/s  Height 5,296.451 km.
;;;                   Orbital velocity for current height is 5.843 km/s  Fuel 995.8 kg.

__________ T 5            Increase orbital velocity - C
Time (s) 14086        Velocity 6.112 km/s  Inclination  1 Degrees  Up velocity -0.781 km/s  Height 5,292.548 km.
;;;                   Orbital velocity for current height is 5.844 km/s  Fuel 712.8 kg.

__________ F 2500         Allow time to drop
Time (s) 16586        Velocity 6.112 km/s  Inclination  1 Degrees  Up velocity -0.651 km/s  Height 3,742.383 km.
;;;                   Orbital velocity for current height is 6.276 km/s  Fuel 712.8 kg.

__________ T 3            Increase orbital velocity - D
Time (s) 16589        Velocity 6.540 km/s  Inclination  1 Degrees  Up velocity -0.651 km/s  Height 3,740.428 km.
;;;                   Orbital velocity for current height is 6.276 km/s  Fuel 543.0 kg.

__________ F 2900         Allow time to drop
Time (s) 19489        Velocity 6.540 km/s  Inclination  1 Degrees  Up velocity -0.530 km/s  Height 2,432.605 km.
;;;                   Orbital velocity for current height is 6.726 km/s  Fuel 543.0 kg.

__________ T 2            Increase orbital velocity - E
Time (s) 19491        Velocity 6.857 km/s  Inclination  1 Degrees  Up velocity -0.530 km/s  Height 2,431.545 km.
;;;                   Orbital velocity for current height is 6.727 km/s  Fuel 429.8 kg.

__________ F 1000         Allow time to drop
Time (s) 20491        Velocity 6.857 km/s  Inclination  1 Degrees  Up velocity -0.476 km/s  Height 1,953.465 km.
;;;                   Orbital velocity for current height is 6.917 km/s  Fuel 429.8 kg.

__________ T 1            Increase orbital velocity - F
Time (s) 20492        Velocity 7.028 km/s  Inclination  1 Degrees  Up velocity -0.476 km/s  Height 1,952.989 km.
;;;                   Orbital velocity for current height is 6.917 km/s  Fuel 373.2 kg.

__________ F 1000         Allow time to drop
Time (s) 21492        Velocity 7.028 km/s  Inclination  1 Degrees  Up velocity -0.448 km/s  Height 1,517.928 km.
;;;                   Orbital velocity for current height is 7.105 km/s  Fuel 373.2 kg.

__________ T 1            Increase orbital velocity - G
Time (s) 21493        Velocity 7.207 km/s  Inclination  1 Degrees  Up velocity -0.448 km/s  Height 1,517.480 km.
;;;                   Orbital velocity for current height is 7.105 km/s  Fuel 316.6 kg.

__________ F 900          Allow time to drop
Time (s) 22393        Velocity 7.207 km/s  Inclination  1 Degrees  Up velocity -0.423 km/s  Height 1,147.043 km.
;;;                   Orbital velocity for current height is 7.278 km/s  Fuel 316.6 kg.

__________ T 1            Increase orbital velocity - H
Time (s) 22394        Velocity 7.396 km/s  Inclination  1 Degrees  Up velocity -0.423 km/s  Height 1,146.620 km.
;;;                   Orbital velocity for current height is 7.278 km/s  Fuel 260.0 kg.

__________ F 1620         Allow time to drop and set approx final height
Time (s) 24014        Velocity 7.396 km/s  Inclination  1 Degrees  Up velocity -0.556 km/s  Height 499.663 km.
;;;                   Orbital velocity for current height is 7.613 km/s  Fuel 260.0 kg.

__________ P 43.3275      Fine tune final speeds
Time (s) 24015        Velocity 7.396 km/s  Inclination  1 Degrees  Up velocity -0.556 km/s  Height 499.107 km.
;;;                   Orbital velocity for current height is 7.613 km/s  Fuel 260.0 kg.

__________ T 2            Increase orbital velocity - I
Time (s) 24017        Velocity 7.696 km/s  Inclination  1 Degrees  Up velocity -0.274 km/s  Height 498.273 km.
;;;                   Orbital velocity for current height is 7.614 km/s  Fuel 146.8 kg.

__________ F 627          Allow time to drop - accerate height setting
Time (s) 24644        Velocity 7.696 km/s  Inclination  1 Degrees  Up velocity -0.218 km/s  Height 350.030 km.
;;;                   Orbital velocity for current height is 7.697 km/s  Fuel 146.8 kg.

__________ P 90           Park satellite
Time (s) 24645        Velocity 7.696 km/s  Inclination  1 Degrees  Up velocity -0.218 km/s  Height 349.811 km.
;;;                   Orbital velocity for current height is 7.697 km/s  Fuel 146.8 kg.

__________ T 1            Slow down
Time (s) 24646        Velocity 7.696 km/s  Inclination  1 Degrees  Up velocity 0.008 km/s  Height 349.706 km.
;;;                   Orbital velocity for current height is 7.697 km/s  Fuel 90.2 kg.

__________ F 100          Allow time to drop
Time (s) 24746        Velocity 7.696 km/s  Inclination  1 Degrees  Up velocity 0.008 km/s  Height 350.476 km.
;;;                   Orbital velocity for current height is 7.697 km/s  Fuel 90.2 kg.

__________ F 100          Verify that satellite is still in orbit
Time (s) 24846        Velocity 7.696 km/s  Inclination  1 Degrees  Up velocity 0.007 km/s  Height 351.229 km.
;;;                   Orbital velocity for current height is 7.696 km/s  Fuel 90.2 kg.

Fuel left  90.2001419067383 kg.

*END

High drop to LEO does not work as a fuel saving measure.  The fuel saved by the height is wasted on the large amount of fuel needed to remove the order of magnitude greater vertical delta_v due to gravity.

____________________ Testing effect of launching a satellite from the Space Elevator

Dropping a 300 kg Pay Load to 350 km from 10,000 km

Satellite is to be thrown at a height of 10,000.000 km whilst raising at a speed of 147.000 km/h or 0.041 km/s.
Moving climber to  10000 km takes  2 days  2 Hours and  0 minutes at 200 km/h

Aiming satellite at a final height of  350 km and an inclination of  1 degrees.
Therefor orbital velocity needs to be 7.697 km/s
The Pay Load weighs 300.0 kg, fuel 5,354.0 kg and the structure  420 kg.
Total mass at launch is 6,074.0 kg.
Thrust of rocket 196 kN and fuel burn rate 56.6 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 1.194 km/s.

Command types
F = Freefall for 'Value' seconds
I = Change Inclination by 'Value' degrees.  Negative to go south
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
T = Thrust for 'Value' seconds or until the fuel runs out


Time (s) 0            Velocity 1.194 km/s  Inclination  0 degrees  Up velocity 0.041 km/s  Height 10,000.000 km

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 1.194 km/s  Inclination  0 Degrees  Up velocity 0.035 km/s  Height 10,000.152 km.

__________ P 5.3          Select angle to counter gravity
Time (s) 5            Velocity 1.194 km/s  Inclination  0 Degrees  Up velocity 0.034 km/s  Height 10,000.187 km.

__________ I 1            Fly to the new orbit of 1 degree inclination
Time (s) 6            Velocity 1.194 km/s  Inclination  1 Degrees  Up velocity 0.033 km/s  Height 10,000.220 km.

__________ F 3229         Allow time to drop
Time (s) 3235         Velocity 1.194 km/s  Inclination  1 Degrees  Up velocity -7.483 km/s  Height 1,076.084 km.

__________ T 90           Use Thruster to gain required orbital speed
Time (s) 3325         Velocity 7.569 km/s  Inclination  1 Degrees  Up velocity -7.414 km/s  Height 394.744 km.

__________ P -81          Try to stop satellite falling
Time (s) 3326         Velocity 7.569 km/s  Inclination  1 Degrees  Up velocity -7.414 km/s  Height 387.330 km.

__________ T 10000        Use up remaining fuel
Time (s) 3330         Velocity 7.699 km/s  Inclination  1 Degrees  Up velocity -8.239 km/s  Height 355.945 km.

__________ F 5000         Verify that satellite is still in orbit
** Satellite has crashed at  3374 Fuel  0 Kg  velocity  7.699397 km/s  Up Velocity  -8.249663 km/s  Inclination  1 degrees  Height  -6.727885 km.

People will wonder if dropping a satellite from a great height causes it to orbit the Earth faster “Why cannot the entire acceleration be done using this 'free' energy?”  Answer because the height to do it is above GEO.  When released the satellite escapes.  As this example shows, even burning all of the fuel does not stop the expensive satellite flying away from the Earth. :mad:


____________________ Testing effect of launching a satellite from the Space Elevator

High drop of 300 kg to 350 km in LEO.

When thrown the Satellite was raising (falling) at a speed of -200.000 km/h or -0.056 km/s.
Aiming at a final height of  350 km and an inclination of  1 degrees.
Therefor orbital velocity needs to be 7.697 km/s
The Pay Load weighs 300.0 kg, fuel 5,354.0 kg and the structure  420 kg.
Total mass at launch is 6,074.0 kg.
Thrust of rocket 196 kN and fuel burn rate 56.6 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.465 km/s.

Command types
C = Calculate height to generate orbital velocity of final height. (Dummy parameter)
F = Freefall for 'Value' seconds
I = Change Inclination by 'Value' degrees.  Negative to go south
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
T = Thrust for 'Value' seconds or until the fuel runs out


Time (s) 0            Velocity 0.465 km/s  Inclination  0 degrees  Up velocity -0.056 km/s

__________ C 0            Raise to generate the orbital velocity
Moving climber to  99175.37 km.  This takes  20 days  16 Hours and  52.61 minutes at 200 km/h
Time (s) 0            Velocity 7.697 km/s  Inclination  0 Degrees  Up velocity -0.056 km/s  Height 99,175.367 km.

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 7.697 km/s  Inclination  0 Degrees  Up velocity -0.053 km/s  Height 99,175.148 km.

__________ P -15          Select Pitch angle - downwards because at these heights there is a shortage of gravity
Time (s) 5            Velocity 7.697 km/s  Inclination  0 Degrees  Up velocity -0.053 km/s  Height 99,175.094 km.

__________ I 1            Fly to the new orbit of 1 degree inclination
Time (s) 10           Velocity 7.697 km/s  Inclination  1 Degrees  Up velocity -0.092 km/s  Height 99,174.742 km.

__________ F 86400        Free fall for a day
Time (s) 86410        Velocity 7.697 km/s  Inclination  1 Degrees  Up velocity 16.449 km/s  Height 1,090,412.875 km.

__________ P -90          Point thruster to slow satellite down
Time (s) 86411        Velocity 7.697 km/s  Inclination  1 Degrees  Up velocity 16.449 km/s  Height 1,090,429.375 km.

__________ T 100000       Use Thruster to try and slow down escaping satellite
Time (s) 86501        Velocity 7.697 km/s  Inclination  1 Degrees  Up velocity 9.349 km/s  Height 1,091,690.625 km.

__________ F 5            Verify that satellite is still leaving orbit 5 seconds later
Time (s) 86506        Velocity 7.697 km/s  Inclination  1 Degrees  Up velocity 9.349 km/s  Height 1,091,737.500 km.

Fuel left  0 kg.

*END

A comparison between a Space Elevator launch and a Pegasus rocket launch.  This is a valid comparison because both vehicles are using the same engines.

http://www.orbital.com/NewsInfo/Publications/peg-user-guide.pdf
Using the example on Page 25 of the Orbital Sciences Corporation's Pegasus XL User Manual – sending 227 kg to a 741 km polar orbit.  The details on pages 18 and 21 suggest that a fully loaded Pegasus weights 23,130 kg.
Fuel used = 15,014 + 3,925 + 720 = 19,709 kg.

The SE's rocket weighs an estimated 6,297 kg and uses 5,650 kg of the same solid fuel.

5,650 / 19,709 * 100% = 28.67%

The SE rocket uses about a third of the fuel but takes longer to arrive.

Note:  All the examples at the start of this thread have payloads in excess of 227 kg.  This is not accidental, the production Space Elevators will be able to carry much heavier payloads.  Also a company should think carefully before taking a risky course like going into competition with its suppliers and customers.  There are other rocket manufactures.



____________________ Testing effect of launching a satellite from the Space Elevator

Pegasus XL comparison - 227 kg to 741 km polar orbit, page 25 User Manual

Satellite was thrown at a height of 756.600 km whilst raising at a speed of 131.000 km/h or 0.036 km/s.
Aiming at a final height of  741 km and an inclination of  90 degrees.
Therefor orbital velocity needs to be 7.483 km/s
The Pay Load weighs 227.0 kg, fuel 5,650.0 kg and the structure  420 kg.
Total mass at launch is 6,297.0 kg.
Thrust of rocket 196 kN and fuel burn rate 56.6 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.520 km/s.

Command types
F = Freefall for 'Value' seconds
T = Thrust for 'Value' seconds or until the fuel runs out
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
I = Change Inclination by 'Value' degrees.  Negative to go south


Time  0             Velocity 0.520 Inclination  0 Up velocity 0.036 Height 756.600

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 0.520 km/s  Inclination  0 Degrees  Up velocity 0.005 km/s  Height 756.683 km.

__________ P 4.9          Select Pitch angle - slightly upwards to counter gravity
Time (s) 5            Velocity 0.520 km/s  Inclination  0 Degrees  Up velocity -0.003 km/s  Height 756.685 km.

__________ I 90           Fly to the new orbit of 1 degree inclination
Time (s) 27           Velocity 0.520 km/s  Inclination  90 Degrees  Up velocity -0.110 km/s  Height 755.429 km.

__________ T 100000       Use Thruster, until out of fuel, to gain required orbital speed
Time (s) 105          Velocity 7.483 km/s  Inclination  90 Degrees  Up velocity 0.000 km/s  Height 741.040 km.

__________ F 5            Verify that satellite is still in orbit 5 seconds later
Time (s) 110          Velocity 7.483 km/s  Inclination  90 Degrees  Up velocity 0.000 km/s  Height 741.041 km.

Fuel left  0 kg.

*END



Just to show the fuel saving if we stay near the equator – 4,448 kg rather than 5,650 kg.


____________________ Testing effect of launching a satellite from the Space Elevator

Pegasus XL comparison - 227 kg to 741 km Inclination 1 degree

Satellite was thrown at a height of 750.400 km whilst raising at a speed of 111.000 km/h or 0.031 km/s.
Aiming at a final height of  741 km and an inclination of  1 degrees.
Therefor orbital velocity needs to be 7.483 km/s
The Pay Load weighs 227.0 kg, fuel 4,448.0 kg and the structure  420 kg.
Total mass at launch is 5,095.0 kg.
Thrust of rocket 196 kN and fuel burn rate 56.6 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.520 km/s.

Command types
F = Freefall for 'Value' seconds
T = Thrust for 'Value' seconds or until the fuel runs out
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
I = Change Inclination by 'Value' degrees.  Negative to go south


Time  0             Velocity 0.520 Inclination  0 Up velocity 0.031 Height 750.400

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 0.520 km/s  Inclination  0 Degrees  Up velocity -0.000 km/s  Height 750.461 km.

__________ P 4.1          Select Pitch angle - slightly upwards to counter gravity
Time (s) 5            Velocity 0.520 km/s  Inclination  0 Degrees  Up velocity -0.008 km/s  Height 750.457 km.

__________ I 1            Fly to the new orbit of 1 degree inclination
Time (s) 6            Velocity 0.520 km/s  Inclination  1 Degrees  Up velocity -0.014 km/s  Height 750.446 km.

__________ T 100000       Use Thruster, until out of fuel, to gain required orbital speed
Time (s) 84           Velocity 7.483 km/s  Inclination  1 Degrees  Up velocity 0.000 km/s  Height 741.047 km.

__________ F 5            Verify that satellite is still in orbit 5 seconds later
Time (s) 89           Velocity 7.483 km/s  Inclination  1 Degrees  Up velocity 0.000 km/s  Height 741.047 km.

Fuel left  0 kg.

*END

Yes "High Drop for LEO" is next, followed by using Ion thrusters.

The problems with High Drop for LEO are:
a.  The orbit decays so slowly that I had to change my model from a spreadsheet to a computer program.
b.  At 10,000 km the radiation levels are very high so there may be a ban on launching people from that height.  Fortunately there are plenty of cargo launches.
c.  Climbing to 10 times the height will take 10 times as long so the SE operator will want to charge 10 times as much for ribbon time.  A definite trade off between the price of fuel and the price of ribbon time exists.

The weight of fuel may mean that some heavy cargos can only be high dropped - the ribbon will always be weight limited.

Ion thrusters are very fuel efficient but are very slow/weak so they can only be used when the satellite has (nearly) reached orbital speed.  Use them on a LEO launch and the burnt out remains of your cargo will end up in the sea.  It will be interesting to see if solar powered Ion thrusters are viable on High Drop to LEO.

Example 3 – placing a satellite in a Sun-synchronous orbit

A Sun-synchronous orbit is a polar orbit that is in permanent sun light.  Such an orbit requires a big Delta-V.
http://en.wikipedia.org/wiki/Sun-synchronous_orbit

Note:  If you wish to send a satellite to the North Pole the Equator may not be the world's best launch site.

____________________ Testing effect of launching a satellite from the Space Elevator

Satellite into Sun Synchronous (polar) Orbit

Satellite was thrown at a height of 961.800 km whilst raising at a speed of 0 km/h or 0 km/s.
Aiming at a final height of  800 km and an inclination of  90 degrees.
Therefor orbital velocity needs to be 7.452 km/s
The Pay Load weighs 5,500.0 kg, fuel 70,146.0 kg and the structure  1374 kg.
Total mass at launch is 77,020.0 kg.
Thrust of rocket 726 kN and fuel burn rate 219 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.535 km/s.

Command types
F = Freefall for 'Value' seconds
T = Thrust for 'Value' seconds or until the fuel runs out
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
I = Change Inclination by 'Value' degrees.  Negative to go south


Time  0             Velocity 0.535 Inclination  0 Up velocity  0 Height 961.800

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 0.535 km/s  Inclination  0 Degrees  Up velocity -0.029 km/s  Height 961.741 km.

__________ P 15.35        Select vertical flight angle
Time (s) 5            Velocity 0.535 km/s  Inclination  0 Degrees  Up velocity -0.037 km/s  Height 961.708 km.

__________ I 90           Fly to the new orbit of 90 degree (Polar) inclination
Time (s) 77           Velocity 0.535 km/s  Inclination  90 Degrees  Up velocity -0.370 km/s  Height 946.915 km.

__________ T 248          Use Thruster to gain required orbital speed
Time (s) 325          Velocity 7.452 km/s  Inclination  90 Degrees  Up velocity 0.032 km/s  Height 800.270 km.

__________ P -90          Bring the satellite to a vertical halt
Time (s) 326          Velocity 7.452 km/s  Inclination  90 Degrees  Up velocity 0.032 km/s  Height 800.301 km.

__________ T 10000        Fire thruster
Time (s) 327          Velocity 7.452 km/s  Inclination  90 Degrees  Up velocity 0.000 km/s  Height 800.317 km.

__________ F 5            Verify that satellite is still in orbit 5 seconds later
Time (s) 332          Velocity 7.452 km/s  Inclination  90 Degrees  Up velocity 0.000 km/s  Height 800.318 km.

Fuel left  0 kg.

*END

From ground release to a height of 961.8 km at 200 km/h takes (961.8/200)*60 = 288 minutes 32 seconds.  
In order to hit the target location the climber has to wait for the launch window which occurs once per orbit giving a worst case delay of 101 minutes.  
During this wait the climber should open its cargo hold or throw off the protective fairing and aim the cargo in the correct direction.  
From throw to final orbit takes 327 seconds (5 minute 27 seconds)
When the launch window arrives the climber throws the payload.  
Total time = 288'32 + 101 + 0 + 5'27 =  394'59 minutes (6 hours 35 minutes)
At throw time the climber needs to accurately correct for all rotations and swings in the ribbon.  
The recoil from throwing 77 metric tons is high and must not damage the cable.


The cargo needs to be throw off the climber to prevent the the rocket motor exhaust burning or contaminating the ribbon. Once thrown the cargo is falling until the end of the burn; if any of the parameters are wrong (out of tolerance) the cargo will be sent to the wrong place or fall back to earth.  The height of the throw, climber upward velocity and angle above the horizontal help determine the final height.  The fuel burnt, engine type and time of throw are the prime determents of the actual orbit.  There are interactions between the parameters.

These simulations used the data from Orion rockets motors.

The Orion 50S XL rocket engine is assumed to be have a thrust of 726 kN and to burn 219 kg/s of solid propellent.  Small thrusters to charge course are needed.  In the above sequences the new orbital direction is selected before the rocket is accelerated because this saves fuel.  The structural mass of the rocket is a guess.

The smaller Orion 50 XL rocket engine is assumed to have a thrust of 196 kN and to burn 56.6 kg/s of solid propellent.  This engine can steer itself.  The structural mass is a guess.

After throwing the cargo the empty climbers need handling.  They could be sent to form part of the counterweight, particularly if they can rise under solar power.  They can fall back to the Earth and burn up in the atmosphere.  Being only a few of hours from the ground they can drive back to the Earth, either separately or in convoy.  By parking the climbers a few kilometres above the LEO orbits and bring them back in convoy about 5 LEO launches can be arranged per day, the main cost being a reduction in payloads of the later launches.

Information about rocket motors – see page 21 of
http://www.orbital.com/NewsInfo/Publications/peg-user-guide.pdf

Example 2 – Sending half a ton to the International Space Station.

The International Space Station lives at a nominal height of 360 km (+40/-5) with an orbital inclination of 51.64 degrees in 2006.
http://en.wikipedia.org/wiki/International_Space_Station

The results of simulation 2.


____________________ Testing effect of launching a satellite from the Space Elevator

Half a metric ton to International Space Station using 2 off Orion 50 XL motors

Satellite was thrown at a height of 377.700 km whilst raising at a speed of 150.000 km/h or 0.042 km/s.
Aiming at a final height of  360 km and an inclination of  51.64 degrees.
Therefor orbital velocity needs to be 7.691 km/s
The Pay Load weighs 500.0 kg, fuel 11,450.0 kg and the structure  842 kg.
Total mass at launch is 12,792.0 kg.
Thrust of rocket 392 kN and fuel burn rate 113.11 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.493 km/s.

Command types
F = Freefall for 'Value' seconds
T = Thrust for 'Value' seconds or until the fuel runs out
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
I = Change Inclination by 'Value' degrees.  Negative to go south


Time  0             Velocity 0.493 Inclination  0 Up velocity 0.042 Height 377.700

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 0.493 km/s  Inclination  0 Degrees  Up velocity 0.007 km/s  Height 377.797 km.

__________ P 5.5          Select Pitch angle - slightly upwards to counter gravity
Time (s) 5            Velocity 0.493 km/s  Inclination  0 Degrees  Up velocity -0.002 km/s  Height 377.800 km.

__________ I 51.64        Fly to the same inclination as the International Space Station
Time (s) 19           Velocity 0.493 km/s  Inclination  51.64 Degrees  Up velocity -0.081 km/s  Height 377.221 km.

__________ T 100000       Use Thruster, until out of fuel, to gain required orbital speed
Time (s) 107          Velocity 7.691 km/s  Inclination  51.64 Degrees  Up velocity 0.000 km/s  Height 360.071 km.

__________ F 5            Verify that satellite is still in orbit 5 seconds later
Time (s) 112          Velocity 7.691 km/s  Inclination  51.64 Degrees  Up velocity 0.000 km/s  Height 360.073 km.

Fuel left  0 kg.

*END

From ground release to drive to the wait location at a height of say 376 km at 200 km/h takes (376/200)*60 = 112'48” minutes.  
In order to hit the target location the climber has to wait for the launch window which occurs once per orbit giving a worst case delay of 92 minutes.  
During this wait the climber should open its cargo hold or throw off the protective fairing and aim the cargo in the correct direction.
When the launch window arrives the climber accelerates to 150 km/h and throws the payload at a height of 377.70 km 41 seconds later.
From throw to final orbit takes 107 seconds.
Total time = 112'48” + 92 + 0'41 + 0'107 = 207'16” minutes (3 hours 27 minutes).

At throw time the climber needs to detect and correct for rotations and swings in the ribbon.  Just after the throw the climber has to handle a large change in its centre of gravity.

The empty climber now needs managing.

Comment.  Fine tuning the velocity of the climber is probably easier than accurately adjusting the horizontal angle of the rocket.

The Space Elevator SE can take loads such as communications satellites to Geostationary Earth Orbit (GEO) or send them to other planets.  However most satellites and astronauts only need to get to Low Earth Orbit (LEO), so LEO is likely to be where the money is made.  With a 15 metric ton payload limit the SE can compete with everything but the biggest (and very expensive) rockets.

The SE only achieves orbital speed at GEO so a second stage is needed to boost the payload satellite's speed and give its orbit the required angular orientation.


Example 1 – Launching a 300 kg load to LEO

____________________ Testing effect of launching a satellite from the Space Elevator

Orion 50 XL Motor taking 300 kg to 350 km.

Satellite was thrown at a height of 365.000 km whilst raising at a speed of 147.000 km/h or 0.041 km/s.
Aiming at a final height of  350 km and an inclination of  1 degrees.
Therefor orbital velocity needs to be 7.697 km/s
The Pay Load weighs 300.0 kg, fuel 5,354.0 kg and the structure  420 kg.
Total mass at launch is 6,074.0 kg.
Thrust of rocket 196 kN and fuel burn rate 56.6 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.492 km/s.

Command types
F = Freefall for 'Value' seconds
T = Thrust for 'Value' seconds or until the fuel runs out
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
I = Change Inclination by 'Value' degrees.  Negative to go south


Time  0             Velocity 0.492 Inclination  0 Up velocity 0.041 Height 365.000

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 0.492 km/s  Inclination  0 Degrees  Up velocity 0.006 km/s  Height 365.094 km.

__________ P 5.3          Select Pitch angle - slightly upwards to counter gravity
Time (s) 5            Velocity 0.492 km/s  Inclination  0 Degrees  Up velocity -0.003 km/s  Height 365.095 km.

__________ I 1            Fly to the new orbit of 1 degree inclination
Time (s) 6            Velocity 0.492 km/s  Inclination  1 Degrees  Up velocity -0.009 km/s  Height 365.089 km.

__________ T 100000       Use Thruster, until out of fuel, to gain required orbital speed
Time (s) 100          Velocity 7.697 km/s  Inclination  1 Degrees  Up velocity 0.000 km/s  Height 350.065 km.

__________ F 5            Verify that satellite is still in orbit 5 seconds later
Time (s) 105          Velocity 7.697 km/s  Inclination  1 Degrees  Up velocity 0.000 km/s  Height 350.067 km.

Fuel left  0 kg.

*END

The first 50 miles of the ribbon are in the atmospher.  As a guess the solar panels are being folded away to reduce the atmospheric drag of the climber.  The climber may even need to curve to a point like aircraft and rockets.
http://en.wikipedia.org/wiki/Atmospheric_drag

Flat surfaces at 90 degress to the direction have a very large drag.  Formula 1 racing cars use such surfaces as air brakes.

Hello,
       I am Andrew Swallow, a computer progammer by trade.  I live on the south coast of England.

I have been calculating the fuel required to reach Low Earth Orbits (LEO) from the Space Elevator.  I want to check my equations - when calculating the uplift due to rotational velocity should the vertical speed be ignored?

The vertical velocity mostly comes from gravity, the satellite is falling until the end of the burn.  Using the Space Elevator as a stage 1 reduces the fuel required relative to ground launch fuel.

p.s.  No one has objected so I ignored the vertical speed.

We may not need a trafic law until say the third Space Elevator but it is easier to pass one 10 page law than say five 2 page laws.  There is plenty of time to get the law right.